It would be safe for me to do that, but I have no idea if it would be safe for you. In my case I would save the picture with a file extension that didn't tell others it was in fact a picture of anything, let alone a credit card. That and it's rare that anyone other than me handles my phone, and even rarer that anyone would have my phone long enough to look at visible pictures, let alone a hidden one, unless I was the one showing the pictures.

It should be fine as long as you don't accidentally send the photo to social media or an acquaintance or someone you do not trust.
Also if you have security measures on your phone in case it gets stolen or lost would be wise. And maybe password protect the photo or make it hidden.

It should be fine, if your phone is stolen, they would have to go through your password and if they did have access to it, they would not know the 3 digits on the back. Having something like apple pay is even more dangerous.